Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the form of the finite-dimensional projective representations of an infinite abelian group

Author: N. B. Backhouse
Journal: Proc. Amer. Math. Soc. 41 (1973), 294-298
MSC: Primary 22D12
MathSciNet review: 0318393
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If the locally compact abelian group $ G$ has a finite-dimensional unitary irreducible projective representation with factor system $ \omega $ (i.e. $ G$ has an $ \omega $-rep), then a subgroup $ G(\omega )$ is defined which fulfils three roles. First, the square-root of the index of $ G(\omega )$ in $ G$ is the dimension of every $ \omega $-rep. Secondly, the $ \omega $-reps of $ G$ can be labelled by the dual group of $ G(\omega )$, up to unitary equivalence. Thirdly, the essential projective form of an $ \omega $-rep is determined by a unique projective representation of the finite group $ G/G(\omega )$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22D12

Retrieve articles in all journals with MSC: 22D12

Additional Information

Keywords: Locally compact abelian group, projective representation, factor system, $ \omega $-regular class, $ \omega $-symmetric subgroup
Article copyright: © Copyright 1973 American Mathematical Society